The Z-boson Mass And Its Formula As Multiple Proofs In One Yummy Bowl Of Pudding

Though its origin is disputed, the phrase “the proof of the pudding is in the eating” is popularly attributed to Cervantes 1615 comic novel Don Quixote. And while one can talk about a pudding’s ingredients all they want, the saying’s meaning stays intact when shortened to “the proof is in the pudding” – because that is where you will ultimately find it; if you bother to at least taste it – as it’s the results that count.

Which is unlike a ‘mathematical proof’ obtained by logic alone since one’s pallet will sometimes disagree with what one thinks is a delicious recipe. In this sense, the implied dichotomy is akin to Kepler’s contribution to elliptic geometry, which per se is independent of experience in the sense that elliptic theorems can be constructed and proven without appeals to any physical phenomena. But in practice Kepler refined Copernicus’s resurrected heliocentric heresy of planetary orbits in a manner that just as clearly is non-abstractly physical and empirically testable. Which ultimately is the key characteristic of the ‘scientific method’ or ‘revolution,’ soon further cemented by Newton and Galileo’s discoveries expressing physical laws by experimental confirmation of their mathematical formulation.

This report accordingly will further pare the phrase down to a “Pudding Proof” that employs multiple means of what a mathematical formula represents, not only being theoretically correct in multiple senses, but confirmed to be correct by a clear correspondence with the most precisely measured empirical value in high-energy particle physics, specifically the neutral weak or Z-boson mass. For the Z’s present measured mass value ( of 91187.6 +2.1 MeV (million electron Volts) is what truly represents the operative meaning of this term with respect to being the ultimate result as ‘physical proof’ of the following equation and invariant mass for the Z-boson: Z = 91187.633 MeV = 9u1/8 + ms – mb;
though one then doesn’t really need to know the mass m of the strange and bottom quarks, or the Higgs vacuum minimum u1.

Likewise, how we obtained these other, presently (grossly) “unknown,” values isn’t at issue either, though obviously it was not achieved by empirical measure nor is related to this equation. Which isn’t meant to squelch natural curiosity, as anyone interested in a history of these discoveries is directed to a preceding article ( describing the dimensionless scaling system of physics that generates the gamete of such fundamental physical constants. In any case, assuming I’m not lying (which is just as provable – if any chumps want to make a bet?), these ‘unknown masses’ contribute to this equation to give the above Z-mass that corresponds precisely with its measured mass average. But then this ‘pudding proof’ basically refers not just directly to the Z-mass, but more importantly empirically implies that these three ‘non-given’ or `ill-measured’ fundamental masses are just as precisely determined and confirmed as proven mass values as the Z itself!

And though this empirical pudding proof seems unprecedented with regard to the implication of the validity the precision of a parameter such as a strange or bottom quark mass (that can’t be directly measured anyway), it certainly remains an outstanding example of the validity of empirical measure as the bedrock of scientific method. For the ultimate strength of the dimensionless numerical scaling system that sets it apart from all other modern theoretical ‘models’ is evident from the raft of confirmable predictions it makes – and largely are presently accessible in well-tested standard contexts (such as the Z) that require no greater experimentally contrived studies to ‘test’ whether some “theoretical interpretation” is ‘correct.’

Yet in a related regard, the equation for the Z-mass itself represents multiple theoretical proofs that strengthen the outstanding empirical correspondence with the pudding of its measured mass. The first matter in this regard straddles both spheres in that the predominant observed or theoretical decay products of a weak neutral boson are admixtures of bottom with strange and/or down quarks in heavy mesons, and practically is the only known particle that can directly decay to a strange Bs-meson. Which according to our equation consists of a –e/3-charged b-quark with a +e/3-charged strange antiquark – which thus assures the charge neutrality of a Bs-meson. Then over and above these confirmed theoretical considerations with respect to the equation’s quarks, there looms the fundamental observations of Peter Higgs concerning the origin of mass in general, and specifically with respect to electroweak symmetry breaking by which the weak Z and W gauge bosons acquire a mass from some mechanism while leaving photons massless. The above equation employs the appropriate Higgs field mechanism best called the vacuum minima u1, which is again generically associated with the ‘3rd generation’ bottom of the -1e/3 ‘down quark family,’ in the same sense that the heavier ‘Higgs vacuum doublet’ u2 represents a neutral pair of tops of the +2e/3 ‘up quark family.’ (Incidentally cognoscenti, they saw evidence of the ‘light Higgs boson’ before CERN replaced the lepton collider with the Large Hadron over five years ago, which thankfully will generate the far more fundamental Heavy Higgs scalar – when that pudding is ready to take out of their oven. [So it’s a big deal for them, but it’s just the basic, strongest set parameter in a real system of numeric Planck-scaling – so knowing its mass is no big whoop, I’d say the Nobel should go to the machine itself – i.e. it should be a bigger deal for everyone and God when they witness baryogenesis {creation of nuclear matter over antimatter}]!)

Actually the above equation is one of two expressions for the Z-mass, as the other naturally involves its relation to the charged W-boson mass. The W itself is the predominant decay product from the heavier ‘Higgs vacuum doublet’ of a top/antitop pair where convention has the +2e/3 top imparting its +charge to the W in mediating a transformation to a –1e/3 bottom. So once again the Higgs fields impart their mass to quarks and gauge bosons, where each theoretical argument reinforces others (there being further supporting pudding proofs that involve equations for neutral and charged pairs of B-mesons that reinforce the basic equation for Z-mass, for example.) And each theoretical nuance is of course supported by the latest measures of these mass values. But the mathematical form of these equations give insights into theoretical and predictive empirical realms that are unavailable in any other standard theoretical scheme. Example: I’ll give a hundred dollars (I’d make it more but care too much to be going broke) to anyone who can find a reference containing the above equation for the Z-mass.

Having established that theoretically it’s a perfectly good equation, there should be some possibility it’s not unique. But I highly doubt it would ever have been published, especially without any knowledge of these other parameters; that I can safely assume are within my copyrights if just because of the strength of this Pudding Proof demands it. Which brings us back to the basic meaning of this old saying – the results are in the tasting and eating of the pudding. And the bottom line test of this principle after the above equation has been posted for six years on this web of the so-called information highway is this – I’ve yet to find an individual who is capable of appreciating a pudding full of yummy plums and proofs, let alone anyone who wants to eat any and taste the results for themselves. But real pudding isn’t intended for foolish authorities who only remember how to speak with forked tongue, it’s made for the likes of you and I who experience the joys of eating or speaking with one tongue – yum!

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* (January 11, 2010) Leonard Susskind, discusses the origin of covalent bonds, Coulomb’s Law, and the names and properties of particles.

This course is a continuation of the Fall quarter
on particle physics. The material will focus on
the Standard Model of particle physics, especially
quantum chromodynamics (the theory of quarks) and
the electroweak theory based on the existence of the
Higgs boson. We will also explore the inadequacies
of the Standard Model and why theorists are led to
go beyond it.

This course was originally presented in Stanford’s Continuing Studies program.

Stanford University:

Stanford Continuing Studies:

Stanford University Channel on YouTube:

Lecture 1 | New Revolutions in Particle Physics: Standard Model Lecture 1 | New Revolutions in Particle Physics: Standard Model
Particle physics

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